Problem: Simplify the following expression: $ q = \dfrac{-9}{10} - \dfrac{9z}{z - 3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{z - 3}{z - 3}$ $ \dfrac{-9}{10} \times \dfrac{z - 3}{z - 3} = \dfrac{-9z + 27}{10z - 30} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{9z}{z - 3} \times \dfrac{10}{10} = \dfrac{90z}{10z - 30} $ Therefore $ q = \dfrac{-9z + 27}{10z - 30} - \dfrac{90z}{10z - 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-9z + 27 - 90z }{10z - 30} $ Distribute the negative sign: $q = \dfrac{-9z + 27 - 90z}{10z - 30}$ $q = \dfrac{-99z + 27}{10z - 30}$